Preprint 31/2004

A notion of Euler characteristic for fractals

Marta Llorente and Steffen Winter

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Submission date: 14. May. 2004
Pages: 31
published in: Mathematische Nachrichten, 280 (2007) 1/2, p. 152-170 
DOI number (of the published article): 10.1002/mana.200410471
MSC-Numbers: 28A80, 52A38, 26B15
Keywords and phrases: euler characteristic, self-similar sets, renewal theorem
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A notion of (average) fractal Euler number for subsets in the Euclidean space with infinite singular complexes is introduced by means of rescaled Euler numbers of infinitesimal r-neighbourhoods. For certain classes of self-similar sets we calculate the associated Euler exponent and the (average) fractal Euler number with the help of the renewal theorem. Examples like the Sierpinski gasket or carpet are provided.

03.07.2017, 01:41